Chapter 8.2, Problem 60IP

To determine

The solution of the equation $\frac{3}{4}x+1.5=2.7$

Answer to Problem 60IP

  $x=4.26$

Explanation of Solution

Given:

The equation, $\frac{3}{4}x+1.5=2.7$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $\frac{3}{4}x+1.5=2.7$ for the variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on left side, first subtract both sides by $1.5$ and then divide both sides by $\frac{3}{4}$ and then simplify further as shown below,

  $\begin{array}{c}\frac{3}{4}x+1.5=2.7\\ \frac{3}{4}x+1.5-1.5=2.7-1.5\\ \frac{3}{4}x=1.2\\ \frac{\frac{3}{4}x}{\frac{3}{4}}=\frac{1.2}{\frac{3}{4}}\\ x=\frac{12.8}{3}\\ x=4.26\end{array}$

Thus, the solution of the given equation is $x=4.26$ .